Rocklin S, Oster G
J Math Biol. 1976 Nov 25;3(3-4):225-61. doi: 10.1007/BF00275058.
We present two models for phenotypic-dependent interspecific competition. In both cases the survivorship of individuals of one population depends on the entire phenotypic distribution of the other species. The first model considers a continuously varying metric trait, with assortative or random mating; the second model examines a character controlled by two alleles at a single locus. Pursuing the notion that each population maximizes its mean fitness we define a vector-optimum strategy using the concepts of cooperative and competitive optima. It is found that the dynamical constraints placed on the equations of motion by Mendelian genetics often prevent a population from evolving to a strategic optimum. However, for the single locus case with complete dominance, the competitive optimum always coincides with some dynamical equilibrium on the Hardy-Weinberg manifold.
我们提出了两种表型依赖的种间竞争模型。在这两种情况下,一个种群个体的存活率取决于另一个物种的整个表型分布。第一个模型考虑一个连续变化的度量性状,交配方式为选型交配或随机交配;第二个模型研究由单个基因座上的两个等位基因控制的性状。基于每个种群将其平均适应度最大化这一观点,我们使用合作最优和竞争最优的概念定义了一种向量最优策略。研究发现,孟德尔遗传学对运动方程施加的动力学约束常常会阻止一个种群进化到策略最优状态。然而,对于完全显性的单基因座情况,竞争最优总是与哈迪 - 温伯格流形上的某个动力学平衡相重合。